ECCC-Report TR24-111https://eccc.weizmann.ac.il/report/2024/111Comments and Revisions published for TR24-111en-usMon, 01 Jul 2024 21:59:13 +0300
Paper TR24-111
| An XOR Lemma for Deterministic Communication Complexity |
Siddharth Iyer,
Anup Rao
https://eccc.weizmann.ac.il/report/2024/111 We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log rk(f)} -\log rk(f)\Big )$, where here $D(f), D(f^{\oplus n})$ represent the deterministic communication complexity, and $rk(f)$ is the rank of $f$. Our methods involve a new way to use information theory to reason about deterministic communication complexity. Mon, 01 Jul 2024 21:59:13 +0300https://eccc.weizmann.ac.il/report/2024/111